Selection of superior soybean genotypes across locations and years in Zimbabwe according to multitrait ideotype
Introduction
Question
How to select superior soybean genotypes across locations and years (GxE interaction) according to Multitrait ideotype? (Simultaneous selection)
Hypothesis
Estimate probability of superior performance (Dias et al. 2022) across locations and years and classify genotypes using Bayesian Probabilistic Selection Index (Chagas et al. 2025)
Goal
Important
Select superior soybean genotypes to grain yield, plant height and plant lodging using Bayesian probabilistic selection index (BPSI) (Chagas et al. 2025)
Material and Methods
- 14 locations
- 6 years
- 41 trials
- 98 genotypes
- 3 traits (Grain Yield, Plant Height, Plant Lodging)
- Randomized complete block design (RCB)
- Using package ProbBreed (Chaves et al. 2024)
Material and Methods
Individual analyses
\[ \mathbf{y} = \mathbf{X_1b} + \mathbf{Z_1g} + \mathbf{\epsilon} \]
where \(\mathbf{y}\) is the vector of phenotypic observations, \(\mathbf{b}\) is the vector of fixed effects of replication, \(\mathbf{g}\) is the vector of random effects of genotypes and \(\mathbf{\epsilon}\) is the vector of random errors. \(\mathbf{X_1}\), \(\mathbf{X_2}\) e \(\mathbf{Z_1}\) are incidence matrix of \(\mathbf{b}\) and \(\mathbf{g}\) effects respectively..
Material and Methods
Heritability
\[ h^2 = \sigma^2g / \sigma^2g + \sigma^2e \]
where \(\sigma^2g\) is the genetic variance and \(\sigma_e^2\) is the residual variance.
Experimental Coeficient of Variation
\[ CV = \frac{\sigma_e}{\mu} \times 100 \]
where \(\mu\) is the trait mean.
Material e Métodos
Likelihood ratio test
\[LRT= −2 \times (Log𝐿 - Log L_𝑅)\]
where \(L\) is the maximum point of residual likelihood function of the complete model and \(L_R\) is the same for the reduced model, that is, without the effect to be tested. The LRT value was compared with a tabulated value based on the chi-square table, with one degree of freedom and 0.95 probability.
Material and Methods
Bayesian model
\[ y_{jkhp} = \mu + t_h + l_k + b_{p(k)} + g_j + gl_{jk} + gt_{jh} + \varepsilon_{jkhp} \] where the \(y_{jkhp}\) is the phenotypic record of the \(j^{th}\) genotype, allocated in the \(p^{th}\) block, in the \(k^{th}\) location and in the year \(t_{th}\). All other effects were previously defined but \(b_{p(k)}\), which is the effect of the \(p^{th}\) block in the \(k{th}\) location, and \(gl^{jk}\) , which correspond to the genotype-by-location interaction \(t_h\) and \(t_{jh}\) are the main effect of years and the genotypes-by-years interaction effect, respectively.
Material and Methods
Probability of superior performance
BPSI index uses the probability of superior performance to estimate the chance of a genotype being selected in multienvironmental trials (Dias et al. 2022).
\[ Pr\left({\hat{g}}_i \in \Omega \middle| y\right) = \frac{1}{s}\sum_{s=1}^{s} I \left({\hat{g}}_i^{(s)} \in \Omega \middle| y\right) \]
where \(\hat{g}_i\) is the genotypic value, \(\Omega\) is a subset of genotypes with superior performance and \(s\) represents each sample of posterior distribution.
Material and methods
Bayesian Probabilistic Selection Index
\[ BPSI_i = \sum_{m=1}^{t} \frac{RankProbSup^t}{\omega^t} \]
where \(t\) is the total number of traits evaluated \((m =1, 2,…,t)\) and \(\omega\) is a weight. Traits of greater interest will have larger \(\omega\). We used weight 2 for GY and weight 1 for PH and PL. The 10% best-ranked families were selected according to the BPSI.
| Genotype | T1(Rank) | T2(Rank) | T3(Rank) | PSI |
|---|---|---|---|---|
| 1 | 10 | 5 | 2 | ∑ i.= 17 |
| 2 | 5 | 3 | 10 | ∑ i.= 18 |
| 3 | 7 | 3 | 10 | ∑ i.= 19 |
Results
Results
Results
Results
Results
Results
Results
Variances
Results
Variances
Results
Density
Results
Within
Results
Across
Results
Density
BPSI
load("../Saves/res_PL_year.rda")
load("../Saves/res_PH_year.rda")
load("../Saves/res_GY_year.rda")
source("../data/bpsi_fun.R")
models= vector("list",length(3))
models[[1]] = res_GY;
models[[2]] = res_PH
models[[3]] = res_PL
models[[3]]$across$perfo <- models[[3]]$across$perfo[-which(models[[3]]$across$perfo$ID=="G_55"),]
names(models) <- c("GY","PH","PL")
BPSI_soy=BPSI(modlist = models,increase =c(TRUE,FALSE,FALSE),omega = c(2,1,1),int = 0.1,save.df = T,verbose = T )
df=BPSI_soy$BPSI
gen.sel = df[which(df$sel=="selected"),"gen"]
real.names=distinct(pheno[,c(5,15)])
df <- left_join(df, real.names, by = c("gen" = "geno"))
print(df) GY PH PL bpsi sel gen Crop_Variety
1 0.5 4.0 4.0 8.5 selected G_20 Opal
2 8.0 6.0 4.0 18.0 selected G_3 Bimha
3 3.0 2.0 17.5 22.5 selected G_38 SBV15043
4 7.0 5.0 18.0 30.0 selected G_45 SC SIESTA
5 13.0 3.0 15.0 31.0 selected G_4 CBI1055/6/6
6 7.0 8.0 24.5 39.5 selected G_13 Mhembwe
7 29.0 12.0 5.0 46.0 selected G_16 Mwenezi
8 19.0 18.0 14.0 51.0 selected G_1 1075/6/2
9 2.0 49.0 1.5 52.5 selected G_32 S1195/6/105
10 19.0 21.5 12.0 52.5 selected G_33 S1219/6/116
11 27.0 7.0 19.0 53.0 not_sel G_14 Mhofu
12 15.0 38.0 4.5 57.5 not_sel G_21 Pan 1867
13 10.0 17.0 33.0 60.0 not_sel G_31 S1187/5/37
14 57.0 1.0 2.5 60.5 not_sel G_54 SSS500
15 2.0 52.0 7.0 61.0 not_sel G_50 SC SZ01
16 17.0 17.5 28.0 62.5 not_sel G_28 S1150/5/22
17 48.0 3.5 11.0 62.5 not_sel G_64 TGx 2002-14DM
18 5.0 47.0 13.0 65.0 not_sel G_93 TGx 2053-22FZ
19 13.0 42.0 13.5 68.5 not_sel G_40 SC SAFARI
20 34.0 24.0 11.5 69.5 not_sel G_49 SC STATUS
21 23.0 25.0 23.0 71.0 not_sel G_60 TGx 2000-305GZ
22 37.0 18.0 17.0 72.0 not_sel G_39 SBV15062
23 20.5 39.0 13.0 72.5 not_sel G_68 TGx 2002-9FM
24 36.0 29.0 8.0 73.0 not_sel G_8 Lukanga
25 24.0 34.0 18.5 76.5 not_sel G_77 TGx 2023-301GZ
26 3.0 61.0 20.0 84.0 not_sel G_53 SI273/6/65
27 18.0 24.0 47.0 89.0 not_sel G_36 S1275/6/59
28 21.0 38.0 30.0 89.0 not_sel G_47 SC SPIKE
29 33.0 20.5 38.0 91.5 not_sel G_52 SCS-1
30 23.0 30.0 39.0 92.0 not_sel G_29 S1180/5/54
31 9.0 28.0 55.0 92.0 not_sel G_44 SC SERENADE
32 14.0 76.0 2.0 92.0 not_sel G_9 Lundi
33 32.0 9.5 51.0 92.5 not_sel G_11 MAKSOY 5N
34 43.0 28.0 21.5 92.5 not_sel G_74 TGx 2014-52GZ
35 11.0 58.0 25.0 94.0 not_sel G_42 SC SEMEKI
36 44.0 13.0 43.5 100.5 not_sel G_58 TGx 2000-126GZ
37 12.0 36.0 53.0 101.0 not_sel G_25 S1079/6/7
38 73.0 10.0 24.0 107.0 not_sel G_67 TGx 2002-3FM
39 11.0 76.0 20.5 107.5 not_sel G_46 SC SIGNAL
40 68.0 23.0 18.0 109.0 not_sel G_10 M667
41 55.0 4.5 50.0 109.5 not_sel G_2 A773
42 49.0 16.0 45.0 110.0 not_sel G_30 S1187/5/25
43 77.0 13.0 21.0 111.0 not_sel G_75 TGx 2014-5GM
44 15.0 53.0 44.0 112.0 not_sel G_92 TGx 2053-15FZ
45 54.0 5.0 54.0 113.0 not_sel G_17 N390
46 10.0 76.0 29.5 115.5 not_sel G_43 SC SENTINEL
47 81.0 5.5 29.0 115.5 not_sel G_5 CLARK-63K
48 31.0 25.0 60.0 116.0 not_sel G_89 TGx 2047-08FZ
49 33.5 22.0 63.0 118.5 not_sel G_6 K872
50 65.0 15.0 40.0 120.0 not_sel G_88 TGx 2045-02FZ
51 8.0 76.0 40.0 124.0 not_sel G_34 S1239/6/135
52 30.5 72.0 22.0 124.5 not_sel G_70 TGx 2014-21FM
53 35.0 76.0 16.0 127.0 not_sel G_63 TGx 2001-3FM
54 51.0 76.0 0.5 127.5 not_sel G_27 S1146/5/25
55 47.0 15.5 66.0 128.5 not_sel G_94 TGx 2076-15FZ
56 45.0 60.0 24.0 129.0 not_sel G_35 S1240/6/288
57 50.0 76.0 3.0 129.0 not_sel G_51 SC1146/5/25
58 20.0 76.0 34.0 130.0 not_sel G_26 S1140/5/4
59 59.0 22.5 52.0 133.5 not_sel G_61 TGx 2001-11DM
60 42.0 38.0 57.0 137.0 not_sel G_91 TGx 2052-21FZ
61 39.0 38.0 64.0 141.0 not_sel G_41 SC SAGA
62 86.0 16.0 41.0 143.0 not_sel G_19 O253
63 31.0 40.0 76.0 147.0 not_sel G_84 TGx 2033-85GZ
64 80.0 27.0 42.0 149.0 not_sel G_97 TGx 2090-14FZ
65 32.0 27.0 90.0 149.0 not_sel G_98 TIKOLORE
66 63.0 23.0 65.0 151.0 not_sel G_72 TGx 2014-43FM
67 38.5 21.0 93.0 152.5 not_sel G_65 TGx 2002-35FM
68 33.0 59.0 62.0 154.0 not_sel G_81 TGx 2033-36GZ
69 56.0 64.0 35.0 155.0 not_sel G_85 TGx 2033-91GZ
70 12.5 76.0 67.0 155.5 not_sel G_73 TGx 2014-49FZ
71 58.0 64.0 39.5 161.5 not_sel G_82 TGx 2033-53GZ
72 60.0 64.0 41.0 165.0 not_sel G_90 TGx 2050-01FZ
73 35.5 72.0 58.0 165.5 not_sel G_48 SC SQUIRE
74 40.5 33.0 93.0 166.5 not_sel G_57 TGx 1991-22F
75 43.0 69.0 56.0 168.0 not_sel G_87 TGx 2033-95GZ
76 26.0 55.0 88.0 169.0 not_sel G_76 TGx 2020-1GZ
77 53.0 28.5 89.0 170.5 not_sel G_80 TGx 2033-25GZ
78 42.0 64.0 68.0 174.0 not_sel G_12 Makwacha
79 34.5 62.0 84.0 180.5 not_sel G_95 TGx 2089-3FZ
80 90.0 76.0 15.5 181.5 not_sel G_24 Panorama 358
81 37.5 70.0 75.0 182.5 not_sel G_18 NASOKO
82 84.0 38.0 61.0 183.0 not_sel G_22 Panorama 29 I
83 86.0 63.0 35.5 184.5 not_sel G_71 TGx 2014-33FM
84 86.0 25.5 73.0 184.5 not_sel G_83 TGx 2033-76GZ
85 70.0 38.0 77.0 185.0 not_sel G_78 TGx 2031-03FZ
86 79.0 18.5 90.0 187.5 not_sel G_56 TGx 1987-62F
87 74.0 70.0 45.0 189.0 not_sel G_96 TGx 2089-8FZ
88 81.0 76.0 36.0 193.0 not_sel G_66 TGx 2002-3DM
89 90.0 22.0 81.0 193.0 not_sel G_7 Kaleya
90 72.0 36.0 86.0 194.0 not_sel G_86 TGx 2033-92GZ
91 45.0 76.0 74.0 195.0 not_sel G_23 Panorama 3
92 90.0 38.0 69.0 197.0 not_sel G_59 TGx 2000-26FZ
93 45.0 76.0 78.0 199.0 not_sel G_37 S882
94 38.0 76.0 85.0 199.0 not_sel G_79 TGx 2033-103GZ
95 45.0 64.0 93.0 202.0 not_sel G_15 MRI DINA
96 90.0 76.0 46.5 212.5 not_sel G_69 TGx 2014-16FM
97 45.0 76.0 93.0 214.0 not_sel G_62 TGx 2001-24FMResults
Highlighting the ranking of probability of superior performance per trait of the selected families.
Figure 1: Ranking of probability of superior performance per trait
Results
Figure 2: Selected families based on BPSI rank
Title?
- Selection of superior soybean genotypes across locations and years in Zimbabwe according to multitrait ideotype
- Multitrait selection of soybean varieties using Bayesian probabilistic selection index
- josetchagas@usp.br
- Obrigado!
Referências
DGM Lab